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The general results presented above for Hamilton's principle can be applied to optics using the Lagrangian defined in Fermat's principle.The Euler-Lagrange equations with parameter σ =x 3 and N=2 applied to Fermat's principle result in ˙ = with k = 1, 2 and where L is the optical Lagrangian and ˙ = /.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
Hamilton's optico-mechanical analogy is a conceptual parallel between trajectories in classical mechanics and wavefronts in optics, introduced by William Rowan Hamilton around 1831. [1] It may be viewed as linking Huygens' principle of optics with Maupertuis' principle of mechanics.
Hamilton's principle is still valid even if the coordinates L is expressed in are not independent, here r k, but the constraints are still assumed to be holonomic. [37] As always the end points are fixed δr k (t 1) = δr k (t 2) = 0 for all k. What cannot be done is to simply equate the coefficients of δr k to zero because the δr k are not ...
Fitts's law is a principle of human movement published in 1954 by Paul Fitts which predicts the time required to move from a starting position to a final target area. Fitts's law is used to model the act of pointing, both in the real world, e.g. with a hand or finger, and on a computer , e.g. with a mouse .
Art historians say Leonardo da Vinci hid an optical illusion in the Mona Lisa's face: she doesn't always appear to be smiling. There's question as to whether it was intentional, but new research ...
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics.
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